Question: Simplify the following expression: $ r = \dfrac{-10}{7} - \dfrac{-10n - 8}{-10} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10}{-10}$ $ \dfrac{-10}{7} \times \dfrac{-10}{-10} = \dfrac{100}{-70} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-10n - 8}{-10} \times \dfrac{7}{7} = \dfrac{-70n - 56}{-70} $ Therefore $ r = \dfrac{100}{-70} - \dfrac{-70n - 56}{-70} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{100 - (-70n - 56) }{-70} $ Distribute the negative sign: $r = \dfrac{100 + 70n + 56}{-70}$ $r = \dfrac{70n + 156}{-70}$ Simplify the expression by dividing the numerator and denominator by -2: $r = \dfrac{-35n - 78}{35}$